where \(\mathcal {M}_{g,n}^{log}\)  is the logarithmic algebraic stack parametrizing stable logarithmic curves of type \((g,n)\) , which is representable by \((\overline{\mathcal {M}}_{g,n},M_{\partial \overline{\mathcal {M}}_{g,n}})\)  by [1]}, and the logarithmic stabilization morphism \(\operatorname{st}^{log}\)  is defined in [2]}.
